By Chandra Mongroo, Ph.D, Full-time Faculty and Doctoral Lecturer, General Education

Writing in mathematics is an essential skill that serves to communicate abstract concepts, proofs, and problem-solving methodologies effectively. Unlike writing in literature, mathematical writing demands precision, clarity, and logical coherence to convey mathematical ideas accurately. This distinct approach to writing underscores the importance of articulating mathematical reasoning and procedures concisely, ensuring that mathematical arguments are both comprehensible and rigorous

Writing an essay in a math class? Not sure where to begin? Here is a helpful resource for engaging in mathematical writing: A Guide to Writing Mathematics (UC Davis).

A General Outline for a Mathematical Essay

  • Introduction: Restate the problem in your own words. Be sure to include vocabulary that is important to the problem.
    • Background Information: Provide context around the problem. Careful not to assume that the reader has full knowledge on the topic. Avoid words such as “obvious” since this assumes the knowledge of your reader. You may include relevant details that will help the reader understand the problem you are presenting. In addition, this section is where specific vocabulary or notation/ symbols are defined. Establishing the definitions, it is safe to use throughout the body of the paper.  
    • Thesis Statement: Restate the goal of the problem in one sentence. This serves as a quick reminder to the reader what you will be attempting to answer. 
  • Body: In this section, you will elaborate your approach and perspective of the problem.
    • Supporting Paragraphs: A good approach to this section would be to break down the problem into various subproblems. The more details that you provide, the more clarity the reader has into your perspective. You should be as elaborate as possible! 
  • Conclusion: This section provides the culminating idea of your paper.
    • Summarize/Review key points: In this section you want to cycle back to the original objective of the problem, that is return to the thesis statement. Provide a small synopsis of your perspective of the problem, and provide emphasis of the conclusion. Make sure that your reader understands how you arrived at your final solution. 
  • Concluding thoughts: You may want to conclude with other ideas that you considered while thinking about the problem. Alternatively, you may leave your reader with questions that you have after the analysis of the problem. This is a good place to provide your experiences of reasoning throughout the problem.